I Have a parallelogram with the vertices $(1,0,1),(3,1,4),(0,2,9)$ and $(-2,1,6)$
I need to find the area of this parallelogram
My Attempt: I understand My end goal is to find the determinant of a matrix formed by these coordinates. So I first translated the whole parallelogram to the origin by subtracting each vertex by $(1,0,1).$
I am left with $(0,0,0),(2,1,3),(-1,2,8)$ and $ (-3,1,5)$
I can ignore the origin point now, but I believe I am suppose to only use 2 vertices. How do I pick these two vertices, I understand I could draw it out, but is there an easier way?
Also can this question be done without translating the vertices?
Best Answer
Ahh Thank You for the hints above. I Was able to solve it:
Vectors (0,0,0) (2,1,3) (-1,2,8) (-3,1,5)
(-3,1,5)-(2,1,3) = (-1,2,8) So these are are two vertices needed to find the determinant.
The determinant is -2i +19j -5k. Take the magnitude of this, which is sqrt(390)
Thanks for the help!